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Israel Oral Olympiad
2017 Israel Oral Olympiad
2
Reduce the Fraction
Reduce the Fraction
Source: Israeli Oral Olympiad #2
January 18, 2017
algebra
Fraction
simplify
Problem Statement
Simplify the fraction:
(
1
4
+
4
)
⋅
(
5
4
+
4
)
⋅
(
9
4
+
4
)
⋅
.
.
.
(
6
9
4
+
4
)
⋅
(
7
3
4
+
4
)
(
3
4
+
4
)
⋅
(
7
4
+
4
)
⋅
(
1
1
4
+
4
)
⋅
.
.
.
(
7
1
4
+
4
)
⋅
(
7
5
4
+
4
)
\frac{(1^4+4)\cdot (5^4+4)\cdot (9^4+4)\cdot ... (69^4+4)\cdot(73^4+4)}{(3^4+4)\cdot (7^4+4)\cdot (11^4+4)\cdot ... (71^4+4)\cdot(75^4+4)}
(
3
4
+
4
)
⋅
(
7
4
+
4
)
⋅
(
1
1
4
+
4
)
⋅
...
(
7
1
4
+
4
)
⋅
(
7
5
4
+
4
)
(
1
4
+
4
)
⋅
(
5
4
+
4
)
⋅
(
9
4
+
4
)
⋅
...
(
6
9
4
+
4
)
⋅
(
7
3
4
+
4
)
.
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